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irinina [24]
3 years ago
13

4. The diagram at right shows the graph of 3x + 4y = 12. The shaded figure is a square, three of whose vertices are on the coord

inate axes. The fourth vertex is on the line. Find
(a) the x- and y-intercepts of the line;
(b) the length of a side of the square.
(c) Show that your point is equidistant from the coordinate axes.

Mathematics
1 answer:
nikklg [1K]3 years ago
5 0

Remark

This is a very interesting question.  Draw a line from the origin to where the upper right vertex of the square touches the line. That line has the property that the its equation is y = x. So the "solution" to the point of intersection is the solution of the two equations.

y =  x            (1)

3x + 4y = 12 (2)

Put x in for y in equation 2

3x + 4x = 12

7x = 12

x = 12/7

x = 1.714

y = 1.714

Problem A

<em><u>x intercept</u></em>

The x intercept occurs when y = 0

3x + 4(0) = 12

3x = 12                Divide by 3

x = 12/3

x = 4

the x intercept = (4,0)

<em><u>y intercept</u></em>

The y intercept occurs when x =0

3(0) + 4y = 12

4y = 12

y = 12/4

y = 3

y intercept = (0,3)

Problem B

x and y both equal 1.714 so they are also the length of the square's side.

Problem C

See solution above. x =y is the key fact.

x = y = 1.714

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Which answer represents the series in sigma notation? −5+(−1)+3+7+11
madam [21]

Answer:

In sigma notation, the series may be represented as,

\sum_{x = 0}^{4}(-5 + 4x)

It is an arithmetic progression with

1st term = -5

common difference = 4

no, of terms = 5

Step-by-step explanation:

The finite series is given by,

-5 + (-1) + 3 + 7 + 11

In sigma notation, the series may be represented as,

\sum_{x = 0}^{4}(-5 + 4x)

It is an arithmetic progression with

1st term = -5

common difference = 4

no, of terms = 5

5 0
3 years ago
Phil has 3 times as many rocks as Peter. Together, they have 48 rocks. How many more rocks does Phil have than Peter?
antoniya [11.8K]
Peter has 12 rocks and Phil has 36 rocks.
Let's say Peter is x.
Phil would be 3x since he has 3 times as many rocks.
3x + x = 48
4x = 48
x = 12
12*3=36
4 0
3 years ago
A survey of 1060 randomly selected US teens ages 13 to 17 found that 605 of them say they have made a new friend online
NikAS [45]

Answer:

The 90% confidence interval for the proportion of all US teens who have made a new friend online is (0.55, 0.60).

Step-by-step explanation:

The complete question is:

A survey of 1060 randomly selected US teens ages 13-17 found that 605 of them say they have made a new friend online.  Find and interpret a 90% confidence interval for the proportion, p, of all US teens who have made a new friend online.

Solution:

In a sample of 1060 randomly selected US teens ages 13 to 17, 605 said they have made a new friend online.

Compute the sample proportion of US teens ages 13 to 17 who said they have made a new friend online as follows:

\hat p=\frac{605}{1060}=0.571

The (1 - α)% confidence interval for population proportion is:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

The critical value of <em>z</em> for 90% confidence interval is:

z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645

*use a z-table.

Compute the 90% confidence interval for the proportion of all US teens who have made a new friend online as follows:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

     =0.571\pm 1.645\sqrt{\frac{0.571(1-0.571)}{1060}}\\=0.571\pm 0.025\\=(0.546, 0.596)\\\approx (0.55, 0.60)

Thus, the 90% confidence interval for the proportion of all US teens who have made a new friend online is (0.55, 0.60).

8 0
3 years ago
Slope -3 passing through points (4, -3)
marta [7]

Answer:

If you're asking for the equation:

y= -3x + 9

Step-by-step explanation:

y = mx + b

(plug in the slope)

y = -3x + b

(plug in the point)

-3 = -3(4) + b

-3 = -12 + b

9 = b

(plug back into the original equation)

y = -3x + 9

7 0
3 years ago
A paperweight in the shape of a rectangular pyramid is shown: A right rectangular pyramid is shown. If a cross section of the pa
blsea [12.9K]

triangle, cross sections are 2D and since perpendicular means "at a 90° angle" to something it and since its perpendicular to the base then it could only be a triangle

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3 years ago
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